The decision to postpone the game was taken after an inspection on Saturday evening, with the Millers players delayed holding off heading to the Midlands until it was reached.
The game had been due to kick off at 3pm on Sunday.
A "senior match official" decided the work on the pitch since Friday's inspection by a local referee had not made it safe for a high-level game.
The Sky Blues are tenants of their home ground, which has been used for rugby sevens matches at the Commonwealth Games. The Games were the reason the match was not played on Saturday.
Sixty-two men’s and women's games were played between July 29 and July 31, and the pitch has unsurprisingly not recovered.
Former Rotherham player and manager Mark Robins - now in charge at Coventry - spoke of his unhappiness with the pitch in his pre-match press conference, and the club mirrored it in a statement on their website.
"We are very frustrated that the pitch at the Arena is not up to standard, and share the huge disappointment that fans, players and staff will feel that our opening home game has been postponed under these circumstances," it read.
"Promised investment by the Arena into a new pitch has unfortunately not materialised over the summer, which has been compounded by concerts on the pitch and then a huge amount of use at the Commonwealth Games last weekend.
"We appreciate the efforts in difficult circumstances that have been made by the grounds staff who work for the Arena."
The football club have long had an uneasy relationship with the 17-year-old arena, twice moving out because of disputes. It is owned by the Wasps Group, whose primary interest is the rugby union team, Wasps, who have played there since 2007.
No date has been set for a rearranged game.
Both clubs were hoping to build on decent starts to the season, with Coventry drawing at Sunderland and Rotherham at home to Swansea City on the opening weekend.
The Football League might now reflect on whether it would have been wiser to start Coventry’s season with two away games, to allow the playing surface more time to recover.